A103813 Partial sums of A102370.

0, 3, 9, 14, 18, 33, 43, 52, 60, 71, 85, 98, 126, 149, 167, 184, 200, 219, 241, 262, 282, 313, 339, 364, 388, 415, 445, 506, 550, 589, 623, 656, 688, 723, 761, 798, 834, 881, 923, 964, 1004, 1047, 1093, 1138, 1198, 1253, 1303, 1352, 1400, 1451, 1505, 1558, 1610, 1673

Offset

0,2

References

Hardy and Wright, Sect. 18.2, for definition of average order.

Links

Table of n, a(n) for n=0..53.

David Applegate, Benoit Cloitre, Philippe Deléham, and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

David Applegate, Benoit Cloitre, Philippe Deléham, and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Formula

The average order of A102370(n) is n + O(log n).

Mathematica

Accumulate[f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; Table[ f[n] + n, {n, 0, 53}] ] (* James C. McMahon, Jan 21 2024 *)

Crossrefs

Cf. A102370.

Sequence in context: A092476 A291641 A071346 * A001968 A305373 A111907

Adjacent sequences: A103810 A103811 A103812 * A103814 A103815 A103816

Keyword

nonn,base

Author

N. J. A. Sloane and David Applegate, Apr 01 2005

Status

approved